Repositioning geostationary satellites

Satellites are launched and put into their intended orbit
longitude positions, where they normally stay for many years. As time passes
and needs change, it can be helpful to move satellites to new orbit longitude
positions. During a satellite's lifetime, typically 15 years, it may be
moved perhaps a couple of times.

The figure above shows the geostationary orbit as the outer black circle. The
satellites are travelling eastwards at 3075 m/sec, to keep up with the
earth's rotation below.

When it is required to initiate a orbit repositioning to a further east longitude
orbit position, there is a need to advance the position gradually in
easterly direction for a while, typically over a few weeks till the new
position is reached.

The method described here starts to lower the orbit of a satellite over the
pacific, so that the satellite goes round the earth faster for a while, then the orbit is raised up again when
the new orbit longitude is reached.

Start by slowing down the satellite at position A. It will now start to
drop down, into an elliptical orbit, and if allowed to do so will come back
up again to the same height, a day later. Rather than that, wait half a day
and slow it down yet more, at B, so that it is now in a circular orbit at lower
height, as indicated by the orange line.

Here it is safe from collisions and will be going round the earth in
less than a whole day, so it will appear to slowly advance its easterly
longitude position as each day passes.

I'm assuming you want to move a satellite, initially over the pacific, by 90 deg further east
in longitude, so it is over the Americas (position D). Long= 270E or 90W.

At C you need to boost the speed up a bit so that half a day
later, the satellite will be higher up (at its apogee) at geostationary height
(35786km). After a further half day it will be back down at C, but crucially, it will be orbiting slower than it was in the higher speed orange orbit.

Wait a few weeks till it opposite America, above 90 east, the Bay of Bengal, near India.

At C you need to boost the speed up a bit so that half a day
later, the satellite will be higher up (at its apogee) at geostationary height
(35786km).

At D you need to speed it up further so that the orbit becomes
circularised. The black geo orbit has a slower rotational orbit period than the orange orbit.

At each of the positions, A, B, C and D thrusters need to be fired directly along
the direction of the orbit. To slow the satellite down you need to use
thrusters facing forwards, to speed up the satellite use thrusters facing
backwards.

The height difference in the figures is greatly exaggerated.

The amount of these thruster firings needs to be sufficient to make the
required change in speed, called "delta V". For example, two burns of 3.5 m/s
are associated with a height change of 186 km and a 2.4 deg per day drift rate.*

If there is a need to move a satellite westwards, the above procedure
is modified to raise it temporarily to a higher orbit, so it gradually goes
backwards in longitude, for a while.